Question

Solve:
Estimate the mass of the earth, given, radius of the earth $=6.4\times {10}^{6}m$, acceleration due to gravity $=9.8m/s^2$ and gravitational constant $=6.67\times {10}^{-11}S.I.$ units.

Answer 1

$g=\frac{GM}{R^2}$

Given, $G=6.67\times {10}^{-11}N{m}^2{kg}^{-2}$

$R=6.4\times {10}^{6}m$

$g=9.8{ms}^{-2}$

$\therefore M=\frac{{gR}^2}{G}=\frac{{9.8\times 6.4\times 6.4\times 10}^{12}}{{6.67\times 10}^{-11}}$

$\approx 6\times {10}^{24}kg$